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   "source": [
    "# 第二次作业第4题\n",
    "作者：赵飞\n",
    "学号：202018019427078\n",
    "日期：2021-04-24"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Optimization terminated successfully.\n         Current function value: -7.945823\n         Iterations: 5\n         Function evaluations: 6\n         Gradient evaluations: 6\nfmin_bfgs()在x= -1.3064401174022369 处求得函数最小值： -7.945823375615214\nfminbound()在x= -1.306440096615395 处求得函数最小值： -7.945823375615237\nbrute()在x= -1.3064093338815792 处求得函数最小值： -7.945823370133184\n"
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "points = [] # 跟踪优化过程\n",
    "# 待求最小值的函数\n",
    "f = lambda x: x**2 + 10*np.sin(x)\n",
    "def f_track(x):\n",
    "    '''封装f，以便跟踪优化过程'''\n",
    "    y = x**2 + 10*np.sin(x)\n",
    "    points.append([x, y])\n",
    "    return y\n",
    "# 待求最小值函数的导数\n",
    "fprime = lambda x: 2*x + 10*np.cos(x)\n",
    "# 0. 绘制待求最小值函数看看\n",
    "x = np.linspace(-10, 10, 100)\n",
    "y = f(x)\n",
    "plt.plot(x, y, label=\"$x^2+10*\\sin{(x)}$\", linewidth=0.5)\n",
    "\n",
    "# 1. 用fmin_bfgs()优化以求最小值\n",
    "points = []\n",
    "r = opt.fmin_bfgs(f_track, 0, fprime=fprime)\n",
    "print(\"fmin_bfgs()在x=\", r[0], \"处求得函数最小值：\", f(r[0]))\n",
    "trace = np.array(points)\n",
    "plt.plot(trace[:,0], trace[:,1], '.', label=\"fmin_bfgs() minimize track\")\n",
    "\n",
    "# 2. 用fminbound()优化以求最小值\n",
    "points = []\n",
    "r = opt.fminbound(f_track, -10, 10)\n",
    "print(\"fminbound()在x=\", r, \"处求得函数最小值：\", f(r))\n",
    "trace = np.array(points)\n",
    "plt.plot(trace[:,0], trace[:,1], '.', label=\"fminbound() minimize track\")\n",
    "\n",
    "# 2. 用brute()优化以求最小值\n",
    "points = []\n",
    "r = opt.brute(f_track, ranges=((-10, 10),))\n",
    "print(\"brute()在x=\", r[0], \"处求得函数最小值：\", f(r[0]))\n",
    "trace = np.array(points)\n",
    "plt.plot(trace[:,0], trace[:,1], '.', label=\"brute() minimize track\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ]
}